1. Field of the Invention
The invention relates to a nano-indentation ultrasonic detection system and method thereof and in particular to a nano-indentation ultrasonic detecting system and method thereof precisely detecting Young's modulus and Poisson's ratio for a material.
2. Description of the Related Art
A conventional nano-indentation system performs indentation experiments on a surface of a material. Information of load and displacement during the indentation experiments are recorded. Mechanical properties, such as indentation hardness and reduced modulus, of the material can thus be obtained. Moreover, by setting the appropriate conditions, other properties, such as adhesion, fracture mechanics, tribology, and fatigue, of the material can also be obtained. Nevertheless, the reduced modulus obtained by the conventional nano-indentation system is a relationship between Young's modulus and Poisson's ratio of the material. The Young's modulus can be determined only by speculating the Poisson's ratio in advance. Accordingly, when the speculated Poisson's ratio differs from the real Poisson's ratio of the material, especially for the thin film for which the Poisson's ratio cannot be detected by conventional experimental approaches, the determined Young's modulus is rendered incorrect.
FIG. 1 is a schematic geometric view of an indenter 10 of a conventional nano-indentation system indenting a surface 21 of a material 20. hmax denotes the maximum indented displacement of the surface 21, generated by the indenter 10. hc denotes the contact depth between the indenter 10 and the surface 21. hs denotes the vertical distance between an initial contact position of the indenter 10 and surface 21 and the initial position of the surface 21 being not indented. hf denotes the residual depth of the surface 21. The hmax, hc, and hs form as:hmax=hc+hs 
FIG. 2 is a diagram showing the relation between the load (P) of the indenter and the displacement (h) of the surface of the material according to FIG. 1. Pmax denotes the magnitude of the load of the indenter 10 at hmax (the maximum indented displacement of the surface 21), a denotes a loading curve of the indenter 10, and b denotes an unloading curve of the indenter 10. Moreover, the unloading curve b can be expressed by an equation as follows:P=K(h−hr)m,
wherein K and m are fitted constants from data of unloading experiments.
Moreover, contact stiffness s is the slope of the unloading curve b at hmax and can be expressed as:
  S  =                              ⅆ          P                          ⅆ          h                    ❘      h        =          h      max      
According to contact mechanics, the reduced modulus (Er) of the indenter 10 and material 20 and a tip area function of an indentation can be expressed as:
            E      r        =                  π        2            ⁢              S        A              ,
wherein A denotes the cross-sectional area of the initial contact position between the indenter 10 and the surface 21.
Additionally, the reduced modulus (Er) can be expressed as:
            1              E        r              =                            1          -                      v            1            2                                    E          1                    +                        1          -                      v            2            2                                    E          2                      ,
wherein E1 and E2 respectively denote the Young's moduli of the indenter 10 and material 20, and v1 and v2 respectively denote the Poisson's ratios thereof.
As depth of an indentation produced by the nano-indentation system is often shallow, precise tip area function of the indentation must be obtained. Oliver and Pharr performed multiple indentation experiments on fused silica and thereby fit the following tip area function according to the data thereof:A(hc)=C0hc2+C1hc1+C2hc1/2+C3hc1/4+ . . . +C8hc1/128,
wherein C0 is the coefficient of the indenter with a perfect geometric shape and C1 to C8 are fitted constants.
Moreover, contact mechanics provides the following formula:
            h      s        =          ɛ      ⁢                        P          max                S              ,
wherein ε is a constant related to the geometric shape of the indenter 10. For example, the ε of the indenter of Berkovich is 0.75. Accordingly, as the material of the indenter 10 is known, the reduced modulus of the indenter 10 and material 20 can be determined by the aforementioned formulae. Nevertheless, the conventional nano-indentation system can only obtain the relation between the Young's modulus and the Poisson's ratio of the material, rather than the respective Young's modulus and Poisson's ratio thereof.
Hence, there is a need for a nano-indentation ultrasonic detecting system and method overcoming the disadvantage of the conventional nano-indentation system detecting the Young's modulus of a material by speculating the Poisson's ratio thereof in advance and avoid obtaining inaccurate Young's modulus thereof.